Related papers: Patterns in treeshelves
We study the growth of a time-ordered rooted tree by probabilistic attachment of new vertices to leaves. We construct a likelihood function of the leaves based on the connectivity of the tree. We take such connectivity to be induced by the…
Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the present work, we define and study a new subclass of tree-like…
We examine the distribution and popularity of different parameters (such as the number of descents, runs, valleys, peaks, right-to-left minima, and more) on the sets of increasing and flattened permutations. For each parameter, we provide…
The relationship between two important problems in tree pattern matching, the largest common subtree and the smallest common supertree problems, is established by means of simple constructions, which allow one to obtain a largest common…
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees ("Otter trees"), when trees of a given size are taken with equal likelihood. The height of a rooted tree of size $n$ is proved to…
Rooted phylogenetic networks allow biologists to represent evolutionary relationships between present-day species by revealing ancestral speciation and hybridization events. A convenient and well-studied class of such networks are…
A tanglegram consists of two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the trees. We show that the two halves of a random tanglegram essentially look like two independently chosen random…
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
We enumerate and characterize some classes of alternating and reverse alternating involutions avoiding a single pattern of length three or four. If on one hand the case of patterns of length three is trivial, on the other hand, the length…
In this paper, the problem of pattern avoidance in generalized non-crossing trees is studied. The generating functions for generalized non-crossing trees avoiding patterns of length one and two are obtained. Lagrange inversion formula is…
We prove limit laws for the number of occurrences of a pattern on the fringe of a ranked tree-child network which is picked uniformly at random. Our results extend the limit law for cherries proved by Bienvenu et al. (2022). For patterns of…
We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…
We study several enumeration problems connected to linear trees, a broad class which includes stars, paths, generalized stars, and caterpillars. We provide generating functions for counting the number of linear trees on $n$ vertices,…